A pair of dice is thrown 7 times. If getting a total of 7 is considered a success, the probability of exactly 6 successe, is:

Let \(A=\left[a_{i j}\right]_{3 \times 3}\) be a matrix, defined by \(a_{i j}=\left\{\begin{array}{ll}2 i+3 j & , i < j \\ 6 & , i=j \\ 3 i-2 j & , i > j\end{array}\right.\). The number of elements in A. which are greater than 6, is

Rakshita plans to buy a house for Rs. 1,00,00,000 with down payment of 20% of the value of the house paid by her mother. Rest of the amount she wishes to pay in 25 years by equal monthly instalments at an interest of 9% per annum compounded monthly Then the EMI paid by her is \(\left(\right.\) Given \(\left.(1.0075)^{300}=9\right)\) :

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) be vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=3,|\vec{b}|=5\) and \(|\vec{c}|=7\), then the angle between \(\vec{a}\) and \(\vec{b}\) is

If \(x=t^2\) and \(y=t^3\), then \(\frac{d y}{d x}=6\) at \(t=\)

If \(y=x^2 \log x\) then \(\frac{d^2 y}{d x^2}=\)

If \(\left|\begin{array}{ll}x & 8 \\ 4 & x\end{array}\right|=\left|\begin{array}{cc}6 & 2 \\ 18 & 6\end{array}\right|\), then \(x\) is/are equal to:

The mean of the number of heads in a simultaneous toss of three coins is :

\(\mathrm{Cr}_2 \mathrm{O}_7^{2-}\) dissolves in aqueous NaOH to give:

The value of the determinant \(\left|\begin{array}{ccc}66 & 18 & 36 \\ 1 & 3 & 4 \\ 11 & 3 & 6\end{array}\right|\) is:

Match List-I with List-I

List-I	List-II
A. Electric field outside a uniformly charged thin spherical shell	(I) zero
B. Electric field inside a uniformly charged thin spherical shell	(II) \(\frac{\lambda}{2 \pi \epsilon_0 r} \vec{n}\)
C. Electric field due to an infinitely long straight uniformly charged wire	(III) \(\frac{\sigma}{2 \epsilon_0} \vec{n}\)
D. Electric field due to a uniformly charged infinite plane sheet	(IV) \(\frac{k q}{r^2} \vec{r}\)

Choose the correct answer from the options given below:

Read the passage carefully and answer the Questions
According to Valence Bond theory, the metal atom or ion under the influence of ligands can use its ( \(n-1) d, n s, n p\) or \(n s, n p, n d\) orbitals for hybridisation to yield a set of equivalent orbitals of definite geometry such as octahedral, tetrahedral, square planar and so on. These hybridised orbitals are allowed to overlap with ligand orbitals that can donate electron pairs for bonding. While the VB theory, to a larger extent, explains the formation, structures and magnetic behaviour of coordination compounds, it suffers from the many shortcomings. The Crystal field theory (CFT) is an electrostatic model which considers the metal-ligand bond to be ionic arising purely from electrostatic interactions between the metal ion and the ligand. The five \(d\) orbitals in an isolated gaseous metal atom/ion have same energy, i.e., they are degenerate. This degeneracy is maintained if a spherically symmetrical field of negative charges surrounds the metal atom/ion. However, when this negative field is due to ligands in a complex, it becomes asymmetrical and the degeneracy of the \(d\) orbitals is lifted. It results in splitting of the \(d\) orbitals. The pattern of splitting depends upon the nature of the crystal field.
Which of the following represents the correct pair?

In experimental arrangement to study photoelectric effect, here M, N, O and P respectively are

(A) Commutator
(B) Evacuated glass tube
(C) Quartz window
(D) Photosensitive plate
Choose the correct answer from the options given below: